Means and Deviations

# ENVS 202 On-line Access

## Sample Means and Deviations

In class exercise. Class do the following:

- Draw a number from the Sacred Box of Sampling in the
front of the Lecture room
- Return to your seat with that number and note your seat number
- Be prepared to tell the instructor your number if your
seat numbers is randomly called
- That is all

In the
Sacred Box of Sampling there are 170 numbers which
define this Intrinsic Distribution .

The point of the in class exercises is to demonstarte that a
random sampling process done for an intrinsic distribution which
is normally distributed (i.e. a bell curve)
will provide a robust estimate of the mean and dispersion after
just a small number of samples.. While
this can be proved with calculus (and in statistics is known as
the
Central Limit Theorem), the in class example is the probably the best
means of demonstrating this.

For this sample as a whole:

- The mean = 175
- The dispersion = 23

The point of the demo in the class is to see how close we can come
to recovering this population mean and dispersion from the sample
mean and dispersion.

In general, we use statistics as a means of characterizing the
nature of some sample on the basis of a few key indicators.

The first indicator is known as
The Sample Mean:

- The mean quantity in some sample represents the average
value or the most probable value in the sample.

- A sample mean is calculated by summing up the individual measurements
and dividing by the number of measurements, usually denoted as N.
- All samples can be characterized by a mean value regardless
of the shape of the distribution

Example:

I open a new store at the Gateway mall that specializes in selling
thematic environmental wallpaper. I notice that there are 6 people
browsing in the store and I ask them their ages. Their ages are:

Use the Tool

The Mean age of the population in the store is 35 years. Does that
tell me much?

The second indicator we use is known as the Sample Variance, also
known as the Sample Dispersion. This is usually denoted by the
greek letter sigma
In general, the dispersion is a more important quantity than the sample
mean. The dispersion represents the range of the data about the mean
value. Understanding the role of dispersion is the most critical
aspect of understanding and interpreting statistical sampling data.

So let's take a look at how dispersion
plays such a critical role.

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